Antithetic variates and quasirandom points as variance reduction techniques

This talk describes how one can transform uniformly distributed quantities to achieve substantive variance reduction in Monte Carlo sampling experiments. An abbreviated historical account of the theory of antithetic variance and the theory of quasirandom points will be presented with emphasis on the identification of circumstances in which results for accelerated error convergence are known in both the univariate and multivariate cases for antithetic variates and quasirandom points. The presentation includes extensions of the theory of antithetic variates to the simulation of Markov chains and semi-Markov processes and the application of quasirandom points to the analysis of stochastic networks. As a special topic, the talk describes how these techniques might fare in the setting of parallel processing.